Question

Ahmad will rent a car for the weekend. He can choose one of two plans. The first plan has an initial fee of $35.98 and costs an additional $0.20 per mile driven. The second plan has an initial fee of $49.98 and costs an additional $0.15 per mile driven. How many miles would Ahmad need to drive for the two plans to cost the same?

Answer 1

If Ahmad travel 280 miles the cost of both plans will be the same

Explanation:

Let's call x the number of miles traveled by Ahmad.

If we say that C1 is the cost of the first plan and C2 is the cost of the second plan then:

C1 = initial fee + additional cost per mile

`C_1 = 35.98 + 0.20x`

C2 = initial fee + additional cost per mile

`C_2 = 49.98 + 0.15x`

We want to know for what value of x, cost 1 will be equal to cost 2. Then we equate the equations and solve for x.

`C_1 = C_2`

`35.98 + 0.20x = 49.98 + 0.15x\\\\0.20x -0.15x = 49.98 -35.98\\\\0.05x = 14\\\\x = 280\ miles`